Pole Placement and Robust Adjustment of Power Systems Stabilizers through Linear Matrix Inequalities

Abstract

This work presents the application of Linear Matrix Inequalities to the optimal adjustment of Power System Stabilizers with pre-defined structure, much common in the power industry. Results of some tests show that gain and zeros adjustments are sufficient to guarantee Power Systems robust stability and performance with respect to various points of operation. Making use of the flexible structure of LMI's, we propose an algorithm that permits one to choose in the compromise between low gain and high damping factor. The technique used here is the pole placement design together with gain limitation, which places the poles of the closed loop system in a specific region of the complex plane. Results of tests with a nine-machine system (New England -New York) are presented and discussed, in order to validate the algorithm proposed.

Applying a robust control technique to damp low frequency oscillations in the WECC

“…One way of implementing such a coordinated control is through the development of an LMI-based polytopic model of the system where time delays are modeled as uncertain parameters, unmeasured portion of the system are represented by un-modeled dynamics, and LMI techniques are used to design robust controllers [15][16][17][18]. The advantage of the polytopic approach is that the span of model uncertainty is considered within the design itself.…”

Co-ordinated control of inter-area oscillations using SMA and LMI

“…As described in the previous chapter, an optimum control for damping Low Frequency Oscillations (LFOs) in general and inter-area modes in particular, can be formulated by using wide area measurements to coordinate PSSs, ESDs, FACTS devices, and DC lines. One way of implementing such an integrated form of control is through the development of an LMI polytopic model of the system where time delays are modeled as uncertain parameters, unmeasured portion of the system are represented by un-modeled dynamics, and LMI techniques are used to design robust controllers [37][38][39][40]. The advantage of the polytopic approach being that the span of the model uncertainty is considered within the design itself.…”

“…An LMI polytopic model has been used to design PSSs for a single machine [37] and a nine bus, threemachine system [38]. Output feedback for a nine machine system was developed in [39]. A design with either full state feedback or output feedback is formulated through a specification of the closed loop pole locations.…”